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Deuterium fractionation can constrain the physical and chemical conditions at the early stage of brown dwarf formation. We present IRAM 30-m observations over a wide frequency range of 213-279 GHz of singly and doubly deuterated species of formaldehyde (HDCO and D₂CO) towards Class 0/I proto-brown dwarfs (proto-BDs). Multiple low-excitation HDCO and D₂CO transition lines with upper energy level <=40 K are detected. The D₂CO/HDCO, HDCO/H₂CO, and D₂CO/H₂CO abundance ratios range between 0.01 and 2.5 for the proto-BDs, similar to the range seen in low-mass protostars. The highest ratios of D₂CO/HDCO ∼1.3-2.5 are measured for two Stage 0 proto-BDs. These objects could possess a warm corino, similar to the few hot corino cases reported among Class 0 protostars. The mean D₂CO/HDCO, D₂CO/H₂CO, and HDCO/H₂CO ratios for the proto-BDs are comparatively higher than the range predicted by the current gas-grain chemical models, indicating that HDCO and D₂CO are formed via grain surface reactions in the dense and cold interiors of the proto-BDs at an early formation stage.